diff -r f06e5a5a4b46 -r a9599d3d7610 src/HOL/Library/AList.thy --- a/src/HOL/Library/AList.thy Thu Nov 05 10:35:37 2015 +0100 +++ b/src/HOL/Library/AList.thy Thu Nov 05 10:39:49 2015 +0100 @@ -18,7 +18,7 @@ to establish the invariant, e.g. for inductive proofs. \ -subsection \@{text update} and @{text updates}\ +subsection \\update\ and \updates\\ qualified primrec update :: "'key \ 'val \ ('key \ 'val) list \ ('key \ 'val) list" where @@ -163,7 +163,7 @@ by (induct xs arbitrary: ys al) (auto split: list.splits) -subsection \@{text delete}\ +subsection \\delete\\ qualified definition delete :: "'key \ ('key \ 'val) list \ ('key \ 'val) list" where delete_eq: "delete k = filter (\(k', _). k \ k')" @@ -215,7 +215,7 @@ by (simp add: delete_eq) -subsection \@{text update_with_aux} and @{text delete_aux}\ +subsection \\update_with_aux\ and \delete_aux\\ qualified primrec update_with_aux :: "'val \ 'key \ ('val \ 'val) \ ('key \ 'val) list \ ('key \ 'val) list" where @@ -296,7 +296,7 @@ by(cases ts)(auto split: split_if_asm) -subsection \@{text restrict}\ +subsection \\restrict\\ qualified definition restrict :: "'key set \ ('key \ 'val) list \ ('key \ 'val) list" where restrict_eq: "restrict A = filter (\(k, v). k \ A)" @@ -380,7 +380,7 @@ by (induct ps) auto -subsection \@{text clearjunk}\ +subsection \\clearjunk\\ qualified function clearjunk :: "('key \ 'val) list \ ('key \ 'val) list" where @@ -464,7 +464,7 @@ (simp_all add: clearjunk_delete delete_map assms) -subsection \@{text map_ran}\ +subsection \\map_ran\\ definition map_ran :: "('key \ 'val \ 'val) \ ('key \ 'val) list \ ('key \ 'val) list" where "map_ran f = map (\(k, v). (k, f k v))" @@ -490,7 +490,7 @@ by (simp add: map_ran_def split_def clearjunk_map) -subsection \@{text merge}\ +subsection \\merge\\ qualified definition merge :: "('key \ 'val) list \ ('key \ 'val) list \ ('key \ 'val) list" where "merge qs ps = foldr (\(k, v). update k v) ps qs" @@ -558,7 +558,7 @@ by (simp add: merge_conv') -subsection \@{text compose}\ +subsection \\compose\\ qualified function compose :: "('key \ 'a) list \ ('a \ 'b) list \ ('key \ 'b) list" where @@ -723,7 +723,7 @@ by (simp add: compose_conv map_comp_None_iff) -subsection \@{text map_entry}\ +subsection \\map_entry\\ qualified fun map_entry :: "'key \ ('val \ 'val) \ ('key \ 'val) list \ ('key \ 'val) list" where @@ -745,7 +745,7 @@ using assms by (induct xs) (auto simp add: dom_map_entry) -subsection \@{text map_default}\ +subsection \\map_default\\ fun map_default :: "'key \ 'val \ ('val \ 'val) \ ('key \ 'val) list \ ('key \ 'val) list" where